Testing the independence number of hypergraphs

Michael Langberg

doi:10.1007/978-3-540-27821-4_36

Testing the independence number of hypergraphs

Michael Langberg

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

A k-uniform hypergraph G of size n is said to be ε-far from having an independent set of size pn if one must remove at least εn^k edges of G in order for the remaining hypergraph to have an independent set of size pn. In this work, we present a natural property testing algorithm that distinguishes between hypergraphs which have an independent set of size ≥ pn and hypergraphs which are ε-far from having an independent set of size pn. Our algorithm is natural in the sense that we sample ≃ c(k) ρ^2k/ε³random vertices of G, and according to the independence number of the hypergraph induced by this sample, we distinguish between the two cases above. Here c(k) depends on k alone (e.g. the sample size is independent of n). To the best of our knowledge, property testing of the independence number of hypergraphs has not been addressed in the past.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Klaus Jansen, Sanjeev Khanna, Jose D. P. Rolim, Dana Ron
Publisher	Springer Verlag
Pages	405-416
Number of pages	12
ISBN (Print)	3540228942, 9783540228943
DOIs	https://doi.org/10.1007/978-3-540-27821-4_36
State	Published - 2004
Externally published	Yes

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3122
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

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10.1007/978-3-540-27821-4_36

Cite this

Langberg, M. (2004). Testing the independence number of hypergraphs. In K. Jansen, S. Khanna, J. D. P. Rolim, & D. Ron (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 405-416). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3122). Springer Verlag. https://doi.org/10.1007/978-3-540-27821-4_36

Langberg, Michael. / Testing the independence number of hypergraphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Klaus Jansen ; Sanjeev Khanna ; Jose D. P. Rolim ; Dana Ron. Springer Verlag, 2004. pp. 405-416 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Langberg, M 2004, Testing the independence number of hypergraphs. in K Jansen, S Khanna, JDP Rolim & D Ron (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3122, Springer Verlag, pp. 405-416. https://doi.org/10.1007/978-3-540-27821-4_36

Testing the independence number of hypergraphs. / Langberg, Michael.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Klaus Jansen; Sanjeev Khanna; Jose D. P. Rolim; Dana Ron. Springer Verlag, 2004. p. 405-416 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3122).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Langberg M. Testing the independence number of hypergraphs. In Jansen K, Khanna S, Rolim JDP, Ron D, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2004. p. 405-416. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-27821-4_36

Testing the independence number of hypergraphs

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